A Minimalist Approach to Type-Agnostic Detection of Quadrics in Point Clouds

This paper proposes a segmentation-free, automatic and efficient procedure to detect general geometric quadric forms in point clouds, where clutter and occlusions are inevitable. Our everyday world is dominated by man-made objects which are designed using 3D primitives (such as planes, cones, spheres, cylinders, etc.). These objects are also omnipresent in industrial environments. This gives rise to the possibility of abstracting 3D scenes through primitives, thereby positions these geometric forms as an integral part of perception and high level 3D scene understanding. As opposed to state-of-the-art, where a tailored algorithm treats each primitive type separately, we propose to encapsulate all types in a single robust detection procedure. At the center of our approach lies a closed form 3D quadric fit, operating in both primal & dual spaces and requiring as low as 4 oriented-points. Around this fit, we design a novel, local null-space voting strategy to reduce the 4-point case to 3. Voting is coupled with the famous RANSAC and makes our algorithm orders of magnitude faster than its conventional counterparts. This is the first method capable of performing a generic cross-type multi-object primitive detection in difficult scenes. Results on synthetic and real datasets support the validity of our method.Comment: Accepted for publication at CVPR 201

Imagerie médicale et patrimoine anthropologique : vers un contrôle total de la chaîne des traitements dans l'analyse morphométrique tridimensionnelle

International audienceThe objective of the present paper is to give some data in medical imaging and 3D reconstruction applied in bio-anthropological field. Scanner CT images are a powerful tool to explore internal structures, to reconstruct incomplete bones and to give biomechanical interpretation based on bone morphology. Further, we propose to argument a cultural hypothesis relatively to a deliberate treatment concerning a human boneNous présentons quelques applications de l’imagerie médicale et de la reconstitution 3D dans le domaine de l’anthropologie biologique. L’acquisition et l’exploitation d’images scanner CT permettent d’accéder aux structures internes, de reconstituer des parties manquantes et d’exploiter des caractéristiques bio-mécaniques. Nous proposons également l’argumentation d’une hypothèse culturelle en relation avec un aménagement pratiqué sur un os humain

A novel musculoskeletal joint modelling for orthopaedic applications

This thesis was submitted for the degree of Docter of Philosophy and awarded by Brunel University.The objective of the work carried out in this thesis was to develop analytical and computational tools to model and investigate musculoskeletal human joints. It was recognised that the FEA was used by many researchers in modelling human musculoskeletal motion, loading and stresses. However the continuum mechanics played only a minor role in determining the articular joint motion, and its value was questionable. This is firstly due to the computational cost and secondly due to its impracticality for this application. On the other hand, there isn’t any suitable software for precise articular joint motion analysis to deal with the local joint stresses or non standard joints. The main requirement in orthopaedics field is to develop a modeller software (and its associated theories) to model anatomic joint as it is, without any simplification with respect to joint surface morphology and material properties of surrounding tissues. So that the proposed modeller can be used for evaluating and diagnosing different joint abnormalities but furthermore form the basis for performing implant insertion and analysis of the artificial joints. The work which is presented in this thesis is a new frame work and has been developed for human anatomic joint analysis which describes the joint in terms of its surface geometry and surrounding musculoskeletal tissues. In achieving such a framework several contributions were made to the 6DOF linear and nonlinear joint modelling, the mathematical definition of joint stiffness, tissue path finding and wrapping and the contact with collision analysis. In 6DOF linear joint modelling, the contribution is the development of joint stiffness and damping matrices. This modelling approach is suitable for the linear range of tissue stiffness and damping properties. This is the first of its kind and it gives a firm analytical basis for investigating joints with surrounding tissue and the cartilage. The 6DOF nonlinear joint modelling is a new scheme which is described for modelling the motion of multi bodies joined by non-linear stiffness and contact elements. The proposed method requires no matrix assembly for the stiffness and damping elements or mass elements. The novelty in the nonlinear modelling, relates to the overall algorithmic approach and handling local non-linearity by procedural means. The mathematical definition of joint stiffness is also a new proposal which is based on the mathematical definition of stiffness between two bodies. Based on the joint stiffness matrix properties, number of joint stiffness invariants was obtained analytically such as the centre of stiffness, the principal translational stiffnesses, and the principal rotational stiffnesses. In corresponding to these principal stiffnesses, their principal axes have been also obtained. Altogether, a joint is assessed by six principal axes and six principal stiffnesses and its centre of stiffness. These formulations are new and show that a joint can be described in terms of inherent stiffness properties. It is expected that these will be better in characterising a joint in comparison to laxity based characterisation. The development of tissue path finding and wrapping algorithms are also introduced as new approaches. The musculoskeletal tissue wrapping involves calculating the shortest distance between two points on a meshed surface. A new heuristic algorithm was proposed. The heuristic is based on minimising the accumulative divergence from the straight line between two points on the surface and the direction of travel on the surface (i.e. bone). In contact and collision based development, the novel algorithm has been proposed that detects possible colliding points on the motion trajectory by redefining the distance as a two dimensional measure along the velocity approach vector and perpendicular to this vector. The perpendicular distance determines if there are potentially colliding points, and the distance along the velocity determines how close they are. The closest pair among the potentially colliding points gives the “time to collision”. The algorithm can eliminate the “fly pass” situation where very close points may not collide because of the direction of their relative velocity. All these developed algorithms and modelling theories, have been encompassed in the developed prototype software in order to simulate the anatomic joint articulations through modelling formulations developed. The software platform provides a capability for analysing joints as 6DOF joints based on anatomic joint surfaces. The software is highly interactive and driven by well structured database, designed to be highly flexible for the future developments. Particularly, two case studies are carried out in this thesis in order to generate results relating to all the proposed elements of the study. The results obtained from the case studies show good agreement with previously published results or model based results obtained from Lifemod software, whenever comparison was possible. In some cases the comparison was not possible because there were no equivalent results; the results were supported by other indicators. The modelling based results were also supported by experiments performed in the Brunel Orthopaedic Research and Learning Centre

A novel musculoskeletal joint modelling for orthopaedic applications

The objective of the work carried out in this thesis was to develop analytical and computational tools to model and investigate musculoskeletal human joints. It was recognised that the FEA was used by many researchers in modelling human musculoskeletal motion, loading and stresses. However the continuum mechanics played only a minor role in determining the articular joint motion, and its value was questionable. This is firstly due to the computational cost and secondly due to its impracticality for this application. On the other hand, there isn’t any suitable software for precise articular joint motion analysis to deal with the local joint stresses or non standard joints. The main requirement in orthopaedics field is to develop a modeller software (and its associated theories) to model anatomic joint as it is, without any simplification with respect to joint surface morphology and material properties of surrounding tissues. So that the proposed modeller can be used for evaluating and diagnosing different joint abnormalities but furthermore form the basis for performing implant insertion and analysis of the artificial joints. The work which is presented in this thesis is a new frame work and has been developed for human anatomic joint analysis which describes the joint in terms of its surface geometry and surrounding musculoskeletal tissues. In achieving such a framework several contributions were made to the 6DOF linear and nonlinear joint modelling, the mathematical definition of joint stiffness, tissue path finding and wrapping and the contact with collision analysis. In 6DOF linear joint modelling, the contribution is the development of joint stiffness and damping matrices. This modelling approach is suitable for the linear range of tissue stiffness and damping properties. This is the first of its kind and it gives a firm analytical basis for investigating joints with surrounding tissue and the cartilage. The 6DOF nonlinear joint modelling is a new scheme which is described for modelling the motion of multi bodies joined by non-linear stiffness and contact elements. The proposed method requires no matrix assembly for the stiffness and damping elements or mass elements. The novelty in the nonlinear modelling, relates to the overall algorithmic approach and handling local non-linearity by procedural means. The mathematical definition of joint stiffness is also a new proposal which is based on the mathematical definition of stiffness between two bodies. Based on the joint stiffness matrix properties, number of joint stiffness invariants was obtained analytically such as the centre of stiffness, the principal translational stiffnesses, and the principal rotational stiffnesses. In corresponding to these principal stiffnesses, their principal axes have been also obtained. Altogether, a joint is assessed by six principal axes and six principal stiffnesses and its centre of stiffness. These formulations are new and show that a joint can be described in terms of inherent stiffness properties. It is expected that these will be better in characterising a joint in comparison to laxity based characterisation. The development of tissue path finding and wrapping algorithms are also introduced as new approaches. The musculoskeletal tissue wrapping involves calculating the shortest distance between two points on a meshed surface. A new heuristic algorithm was proposed. The heuristic is based on minimising the accumulative divergence from the straight line between two points on the surface and the direction of travel on the surface (i.e. bone). In contact and collision based development, the novel algorithm has been proposed that detects possible colliding points on the motion trajectory by redefining the distance as a two dimensional measure along the velocity approach vector and perpendicular to this vector. The perpendicular distance determines if there are potentially colliding points, and the distance along the velocity determines how close they are. The closest pair among the potentially colliding points gives the “time to collision”. The algorithm can eliminate the “fly pass” situation where very close points may not collide because of the direction of their relative velocity. All these developed algorithms and modelling theories, have been encompassed in the developed prototype software in order to simulate the anatomic joint articulations through modelling formulations developed. The software platform provides a capability for analysing joints as 6DOF joints based on anatomic joint surfaces. The software is highly interactive and driven by well structured database, designed to be highly flexible for the future developments. Particularly, two case studies are carried out in this thesis in order to generate results relating to all the proposed elements of the study. The results obtained from the case studies show good agreement with previously published results or model based results obtained from Lifemod software, whenever comparison was possible. In some cases the comparison was not possible because there were no equivalent results; the results were supported by other indicators. The modelling based results were also supported by experiments performed in the Brunel Orthopaedic Research and Learning Centre.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Type-constrained robust fitting of quadrics with application to the 3D morphological characterization of saddle-shaped articular surfaces

International audienceThe scope of this paper is the guaranteed fitting of specified types of quadratic surfaces to scattered 3D point clouds. Since we chose quadrics to account for articular surfaces of various shapes in medical images, the models thus estimated usefully extract global symmetry-related intrinsic features in human joints: centers, axes, extremal curvatures. The unified type-enforcing method is based on a constrained weighted least-squares minimization of algebraic residuals which uses a robust and bias- corrected metric. Provided that at most one quadratic constraint is involved, every step produces closed-form eigenvector solutions. In this framework, guaranteeing the occurrence of 3D primitives of certain types among this eigendecomposition is not a straightforward transcription of the priorly handled 2D case. To explore possibilities, we re-exploit a mapping to a 2D space called the quadric shape map (QSM) where the influence of any constraint on shape and type can in fact be studied visually. As a result, we provide a new enforceable quadratic constraint that practically ensures types such as hyperboloids, which helps characterize saddle-like articular surfaces. Application to a database shows how this guarantee is needed to coherently extract the center and axes of the ankle join